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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Coleman–Weinberg potential ： ウィキペディア英語版 Coleman–Weinberg potential The Coleman–Weinberg model represents quantum electrodynamics of a scalar field in four-dimensions. The Lagrangian for the model is $L\; =\; -\backslash frac\; (F\_)^2\; +\; (D\_\; \backslash phi)^2\; -\; m^2\; \backslash phi^2\; -\; \backslash frac\; \backslash phi^4$ where the scalar field is complex, $F\_=\backslash partial\_\backslash mu\; A\_\backslash nu-\backslash partial\_\backslash nu\; A\_\backslash mu$ is the electromagnetic field tensor, and $D\_=\backslash partial\_\backslash mu-(e/\backslash hbar\; c)A\_\backslash mu$ the covariant derivative containing the electric charge $e$ of the electromagnetic field. Assume that $\backslash lambda$ is nonnegative. Then if the mass term is tachyonic, there is a spontaneous breaking of the gauge symmetry at low energies, a variant of the Higgs mechanism. On the other hand if the squared mass is positive, $m^2>0$ the vacuum expectation of the field $\backslash phi$ is zero. At the classical level the latter is true also if $m^2=0$ However as was shown by Sidney Coleman and Erick Weinberg even if the renormalized mass is zero spontaneous symmetry breaking still happens due to the radiative corrections (this introduces a mass scale into a classically conformal theory - model have a conformal anomaly). The same can happen in other gauge theories. In the broken phase the fluctuations of the scalar field $\backslash phi$ will manifest themselves as a naturally light Higgs boson, as a matter of fact even too light to explain the electroweak symmetry breaking in the minimal model - much lighter than vector bosons. There are non-minimal models that give a more realistic scenarios. Also the variations of this mechanism were proposed for the hypothetical spontaneously broken symmetries including supersymmetry. Equivalently one may say that the model possesses a first-order phase transition as a function of $m^2$. The model is the four-dimensional analog of the three-dimensional Ginzburg–Landau theory used to explain the properties of superconductors near the phase transition. The three-dimensional version of the Coleman–Weinberg model governs the superconducting phase transition which can be both first- and second-order, depending on the ratio of the Ginzburg–Landau parameter $\backslash kappa\backslash equiv\backslash lambda/e^2$, with a tricritical point near $\backslash kappa=1/\backslash sqrt\; 2$ which separates type I from type II superconductivity. Historically, the order of the superconducting phase transition was debated for a long time since the temperature interval where fluctuations are large (Ginzburg interval) is extremely small. The question was finally settled in 1982.〔 〕 If the Ginzburg-Landau parameter $\backslash kappa$ that distinguishes type-I and type-II superconductors (see also here) is large enough, vortex fluctuations becomes important which drive the transition to second order. The tricitical point lies at roughly $\backslash kappa=0.76/\backslash sqrt$, i.e., slightly below the value $\backslash kappa=1/\backslash sqrt$ where type-I goes over into type-II superconductor. The prediction was confirmed in 2002 by Monte Carlo computer simulations.〔 〕 == Literature == * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Coleman–Weinberg potential」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.